{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4a5b3533",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "#API Method for clay\n",
    "Gammades_s = 6.5\n",
    "r_0 = 0.134 \n",
    "z = 0 \n",
    "Gamma1 = Gammades_s\n",
    "Cu = 35\n",
    "D = 2*r_0*1000 \n",
    "X1 =z*1000\n",
    "J = 0.5\n",
    "y_c = 2.5*0.005*2*r_0\n",
    "X_R = 6*D/((Gamma1*D/Cu)+J)\n",
    "if X1 <= X_R:\n",
    "    p_u = 3*Cu + Gamma1*X1 +J*Cu*X1/D\n",
    "else:\n",
    "    p_u = 9*Cu\n",
    "p_u\n",
    "API_y = [0*y_c, 0.1*y_c, 0.3*y_c, 1*y_c, 3*y_c, 8*y_c, 0.1, .15 ]\n",
    "API_P1 = [0.00*p_u, 0.23*p_u, 0.33*p_u, 0.50*p_u, 0.72*p_u, p_u, p_u, p_u] \n",
    "P_Y_days = np.loadtxt(\"P_y_0d.csv\", delimiter=\",\")\n",
    "\n",
    "y1 = np.arange(0.00,0.12,0.01)\n",
    "Gong72_x = [0,0.005406437534097106, 0.009972401399184875, 0.01709059401174545, 0.025380283046115334, 0.03590353326273227, 0.04706476043772662, 0.06248146721863866, 0.0876852475851224, 0.1106557876833221]    \n",
    "Gong72_y = [0,20.944555052790342, 30.3518552036199, 40.82413273001508, 49.87644042232278, 59.461236802413275, 69.40102564102564, 79.16331825037707, 89.10310708898949, 98.15541478129715]\n",
    "\n",
    "plt.plot(y1,P_Y_days[:,720],\"--\",linewidth=2.5,color=\"black\")\n",
    "plt.plot(Gong72_x,Gong72_y, '-',marker='d',linewidth=1.5,color=\"cornflowerblue\")\n",
    "plt.plot(API_y,API_P1,\":\",linewidth=2.5,color=\"black\")\n",
    "plt.xlabel('Pile head displacement (m)',color=\"black\")\n",
    "plt.ylabel(\"Lateral load (kN/m)\",color=\"black\")\n",
    "plt.text(0.005,138,'72 days after pile installation' )\n",
    "plt.legend(['Analytical solution (present study)', \"Field observation\\n(Chaosittichai and Anantanasakul, 2018)\", \"API  method\"],frameon=False)\n",
    "plt.xlim(-0.001,  0.11)\n",
    "plt.ylim(0, 150)\n",
    "plt.rcParams[\"figure.figsize\"] = (7.5,5)\n",
    "plt.rcParams.update({'font.size': 15})\n",
    "plt.rc('font',family='Times New Roman')\n",
    "plt.savefig(\"Fig validation 6d 72days.svg\", format=\"svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "517f68d3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "914168e8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
